Abstract

Using a generalized design for a polarization-sensitive optical coherence tomography (PS-OCT) system with a single input polarization state (SIPS), we prove the existence of an infinitely large design space over which it is possible to develop simple PS-OCT systems that yield closed form expressions for birefringence. Through simulation and experiment, we validate this analysis by demonstrating new configurations for PS-OCT systems, and present guidelines for the general design of such systems in light of their inherent inaccuracies. After accounting for systemic errors, alternative designs exhibit similar performance on average to the traditional SIPS PS-OCT system. This analysis could be extended to systems with multiple input polarization states and could usher in a new generation of PS-OCT systems optimally designed to probe specific birefringent samples with high accuracy.

Poincaré sphere representation of the calculation of birefringence. (a) Transformed light from the source (Ssrc) to the sample (Sin) is rotated by the sample (Sout) prior to measurement (SI(z)). (b) A birefringent sample with optic axis θ rotates Sin about the vector [cos(2θ), sin(2θ),0], tracing out an arc of a circle on the sphere. (c) Optic axθ is proportional to the angle between the +U axis and (S′in − S′out), the projection of Sin − Sout in the Q-U plane. (d) Retardance η is proportional to the angle between S″in and S″out, where S″x is the projection of Sx in the plane with normal vector [cos(2θ), sin(2θ),0] and containing point (cos(2θ), sin(2θ),0).

Effects of polarization properties of the system on the accuracy of the birefringence measurement. (a) Simulated absolute retardance and optic axis error for the systems described in Table 1. Error is associated with a noisy version of the A-scan vector from Eq. 6 and locations of large error depend on Ein (
Media 1 and
Media 2). (b) Location of nodes (black, associated with H: horizontal and V: vertical polarization states) and convergence loci (dashed lines) in the retardance-optic axis space. Nodes typically depress error; convergence loci lead to increased error. (c) Convergence points on Poincaré sphere (arrows) associated with the convergence loci in (b), derived from the intersections of contour lines for optic axis (black) and/or retardance (gray); the location of the H node (red circle) is independent of the system design. (d) Average absolute error (mean of logarithm) across the whole retardance-optic axis space as a function of the polarization state of Er, modeled as a linear polarizer (LP) (
Media 3). (e) Average absolute error as a function of the rotation applied by the sample-to-detector Jones matrix (
Jd−s=JdetJsampT), modeled as a QWP (
Media 4).

Measured birefringence parameters for the four experimental systems from Table 1. (a) Raw data. (b) Revised data after compensating for systemic non-idealities. The ideal behavior of these graphs is shown in the first column for comparison.

Absolute error between ideal (set) and actual retardance and optic axis measurements for (a) simulations of compensated systems and (b) experimental data both before and (c) after compensation. Convergence loci for the compensated systems are overlaid as thin black lines in (b) and (c) as a visual aid.

Tables (3)

Table 1 Description of the experimental systems we constructed in terms of their constituent combinations of physical components (Polarization Components) or induced changes in polarization state (Polarization Properties) as described in Fig. 1a

Table 3 Median of the absolute error before (pre) and after (post) compensation for the four implemented systems (rows). Data given are median values taken over all errors in the retardance-optic axis space.

Metrics

Table 1

Description of the experimental systems we constructed in terms of their constituent combinations of physical components (Polarization Components) or induced changes in polarization state (Polarization Properties) as described in Fig. 1a

System

Polarization Components

Polarization Properties

Jsrc

Jref

Jsamp

Jdet

Ein

Er

Jd−s

Trad

Pol90°

QWP22.5°

QWP45°

none

LeftCP

LP45°

QWP45°

CP

Pol45°

none

QWP90°

none

LeftCP

LP−45°

QWP90°

LP

Pol22.5°

QWP33.75°

none

none

LP22.5°

LP−45°

identity matrix

EP

Pol45°

none

QWP112.5°

none

EP22.5°

LP−45°

QWP112.5°

a Traditional system is abbreviated as Trad; the other systems are named by their input polarization state - CP: circularly polarized, LP: linearly polarized and EP: elliptically polarized.
Jd−s=JdetJsampT gives the Jones matrix that transforms light from the sample prior to reaching the detector. Pol: linear polarizer QWP: quarter waveplate.

Table 2

Summary of the parameters varied to test the contribution of different polarization properties by simulating modification of the traditional system from Table 1

Simulation Type

System Polarization Properties

Ein

Er

Jd−s

Ein

vary from CP to LP

LP 45°

QWP 45°

Er

Left CP

vary LP orientation

QWP 45°

Jd−s

Left CP

LP 45°

vary QWP orientation

Table 3

Median of the absolute error before (pre) and after (post) compensation for the four implemented systems (rows). Data given are median values taken over all errors in the retardance-optic axis space.

System

Retardance Error

Optic Axis Error

Pre

Post

Pre

Post

Trad

1.7°

1.2°

3.4°

2.0°

CP

4.7°

1.2°

7.1°

2.1°

LP

8.4°

1.7°

3.4°

1.5°

EP

5.0°

2.2°

8.6°

2.1°

Tables (3)

Table 1

Description of the experimental systems we constructed in terms of their constituent combinations of physical components (Polarization Components) or induced changes in polarization state (Polarization Properties) as described in Fig. 1a

System

Polarization Components

Polarization Properties

Jsrc

Jref

Jsamp

Jdet

Ein

Er

Jd−s

Trad

Pol90°

QWP22.5°

QWP45°

none

LeftCP

LP45°

QWP45°

CP

Pol45°

none

QWP90°

none

LeftCP

LP−45°

QWP90°

LP

Pol22.5°

QWP33.75°

none

none

LP22.5°

LP−45°

identity matrix

EP

Pol45°

none

QWP112.5°

none

EP22.5°

LP−45°

QWP112.5°

a Traditional system is abbreviated as Trad; the other systems are named by their input polarization state - CP: circularly polarized, LP: linearly polarized and EP: elliptically polarized.
Jd−s=JdetJsampT gives the Jones matrix that transforms light from the sample prior to reaching the detector. Pol: linear polarizer QWP: quarter waveplate.

Table 2

Summary of the parameters varied to test the contribution of different polarization properties by simulating modification of the traditional system from Table 1

Simulation Type

System Polarization Properties

Ein

Er

Jd−s

Ein

vary from CP to LP

LP 45°

QWP 45°

Er

Left CP

vary LP orientation

QWP 45°

Jd−s

Left CP

LP 45°

vary QWP orientation

Table 3

Median of the absolute error before (pre) and after (post) compensation for the four implemented systems (rows). Data given are median values taken over all errors in the retardance-optic axis space.